III. PROBLEM SOLVING $(35$ points$)$

$1.$ Problem $1(5$ points$)$: A steel bar that is $4$ m long and $\backslash (200\backslash$mathrm$\{$~mm$\}^\{2\}\backslash )$ in cross$-$section is subjected to an axial pull of $20$ kN $.$ The Modulus of Elasticity of the bar is $\backslash (\backslash$mathrm$\{$E$\}=200\backslash )$ GPa.

a$.$ Draw the bar showing its length and the external force $(1$ point$)$

b$.$ Convert the length into mm $(1$ point$)$

c$.$ Convert the Load$/$Axial Pull into Newtons $(1$ point$)$

d$.$ Convert the Modulus of Elasticity into $\backslash (\backslash$mathrm$\{$N$\}/\backslash$mathrm$\{$mm$\}^\{2\}\backslash )$

e$.$ Find the elongation of the bar $\backslash (\backslash$delta $\backslash$mathrm$\{$l$\}\backslash )(1$ point$)$

$2.$ Problem $2(5$ points$)$: A brass bar of cross section $\backslash (600\backslash$mathrm$\{$~mm$\}^\{2\}\backslash )$ is acted upon by the forces shown below. For brass, consider E $=200$ GPa.

a$.$ Draw the free body diagram of section A$-$B $(1$ point$)$

b$.$ Draw the free body diagram of section B$-$C $(1$ point$)$

c$.$ Draw the free body diagram of section C$-$D $(1$ point$)$

d$.$ Determine the total elongation of the bar $(2$ points$)$